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Mechanical Advantage
4.2
Mechanical advantage (MA) is the ratio of output force to input force for a machine.
F
MA = ----oFi
or
output force (N)
MA = -----------------------------------input force (N)
Did you notice that the force unit involved in the calculation, the newton (N) is present in both the numerator and
the denominator of the fraction? These units cancel each other, leaving the value for mechanical advantage
unitless.
newtons
N
------------------- = --- = 1
newtons N
Mechanical advantage tells you how many times a machine multiplies the force put into it. Some machines
provide us with more output force than we applied to the machine—this means MA is greater than one. Some
machines produce an output force smaller than our effort force, and MA is less than one. We choose the type of
machine that will give us the appropriate MA for the work that needs to be performed.
Example 1: A force of 200 newtons is applied to a machine in order to lift a 1,000-newton load. What is the
mechanical advantage of the machine?
output force
1000 N
MA = --------------------------- = --------------- = 5
input force
200 N
Machines make work easier. Work is force times distance (W = F × d). The unit for work is the newton-meter.
Using the work equation, as shown in example 2 below, can help calculate the mechanical advantage.
Example 2: A force of 30 newtons is applied to a machine through a distance of 10 meters. The machine is
designed to lift an object to a height of 2 meters. If the total work output for the machine is 18 newton-meters (Nm), what is the mechanical advantage of the machine?
input force = 30 N
output force = ( work ÷ distance ) = ( 18 N-m ÷ 2 m ) = 9 N
output force 9 N
MA = --------------------------- = ---------- = 0.3
input force 30 N
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Mechanical Advantage WS 1/1
4.2
1.
A machine uses an input force of 200 newtons to produce an output force of 800 newtons. What is the
mechanical advantage of this machine?
2.
Another machine uses an input force of 200 newtons to produce an output force of 80 newtons. What is the
mechanical advantage of this machine?
3.
A machine is required to produce an output force of 600 newtons. If the machine has a mechanical
advantage of 6, what input force must be applied to the machine?
4.
A machine with a mechanical advantage of 10 is used to produce an output force of 250 newtons. What input
force is applied to this machine?
5.
A machine with a mechanical advantage of 2.5 requires an input force of 120 newtons. What output force is
produced by this machine?
6.
An input force of 35 newtons is applied to a machine with a mechanical advantage of 0.75. What is the size
of the load this machine could lift (how large is the output force)?
7.
A machine is designed to lift an object with a weight of 12 newtons. If the input force for the machine is set
at 4 newtons, what is the mechanical advantage of the machine?
8.
An input force of 50 newtons is applied through a distance of 10 meters to a machine with a mechanical
advantage of 3. If the work output for the machine is 450 newton·meters and this work is applied through a
distance of 3 meters, what is the output force of the machine?
9.
Two hundred newton·meters of work is put into a machine over a distance of 20 meters. The machine does
150 newton·meters of work as it lifts a load 10 meters high. What is the mechanical advantage of the
machine?
10. A machine has a mechanical advantage of 5. If 300 newtons of input force is used to produce 3,000
newton·meters of work,
a.
What is the output force?
b.
What is the distance over which the work is applied?
Unit 2 Skill and Practice Sheets
4.1 Work Done Against Gravity
1. 1,323 joules
2. 207,000 joules
3. 20 joules
4. 3 meters
5. 3,375 joules
6. 80 kilograms
4.1 Power
1.
2.
3.
4.
5.
6.
7.
8.
9. 2,160,000 joules
10. 2,500 watts
11. 90,000 joules
12. work = 1,500 joules; time = 60 seconds
13. force =25 newtons; power = 250 watts
14. distance = 100 meters; power = 1,000 watts
15. force = 333 newtons, work = 5,000 joules
250 watts
50 watts
1,200 watts
1,500 watts
741 watts
720 watts
work = 500 joules; power = 33 watts
1,800 seconds or 30 minutes
4.2 Mechanical Advantage
1.
2.
3.
4.
5.
6.
7. 3
8. 150 newtons
9. 1.5
10. Answers are:
a. 1,500 newtons
b. 2 meters
4
0.4
100 newtons
25 newtons
300 newtons
26 newtons
4.2 Mechanical Advantage of Simple Machines
1.
2.
3.
4.
5.
6.
7.
8. 6.7
9. 2 meters
10. 12 meters
11. 2.4
12. 6 newtons
13. 560 newtons
14. 4 meters
5
1.5
0.5 meters
4.8 meters
0.4
0.8 meters
0.25 meters
4.2 Gear Ratios
7. Answers for the table are:
Table 2: Set up for three gears
Set Gears Number Ratio 1
up
of teeth
(top
gear:
middle
gear)
1. 9 turns
2. 1 turn
3. 4 turns
4. 10 turns
5. 6 turns
6. Answers for the table are:
Table 1: Using the gear ratio to calculate number of turns
Input
Output
Gear
How many How many
Gear
Gear
ratio
turns does turns does
the input
(# of
(# of
(Input Gear: the output
teeth)
teeth) Output Gear) gear make gear make if
if the input the output
gear turns gear turns 2
3 times?
times?
1
2
Top gear
12
Middle
gear
24
Bottom
gear
36
Top gear
24
24
24
1
3
2
36
12
3
9
0.67, or 2/3
of a turn
Middle
gear
36
24
36
0.67, or 2/3
2
3
12
48
36
1.33, or 4/3
4
1.5
Bottom
gear
24
48
0.5, or 1/2
1.5
4
9
Ratio 2
(middle
gear:
bottom
gear)
Total gear
ratio
(Ratio 1 x
Ratio 2)
1
--2
2
--3
1
--3
2
--3
3
--1
2
--1